Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
540 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C9×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #11721867 | C2 | semidirect |
| 3. #11721865 | C2 | semidirect |
| 4. C2×#88544 | C2 | semidirect |
| 5. #11720575 | C2 | semidirect |
| 6. #11720557 | C2 | semidirect |
| 7. #11720555 | C2 | semidirect |
| 32. C9×AGL(1,ℤ/8) | D3 | semidirect |
| 96. C3×AGL(1,ℤ/8) | D9 | semidirect |
| 197. AGL(1,ℤ/8) | C3⋊D9 | semidirect |
| 203. C3×C9 | #472 | semidirect |
| 280. C9 | #5199 | semidirect |
| 316. C3 | #10588880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×AGL(1,ℤ/8) | 2 |
| #11721867 | 2 |
| #11721865 | 2 |
| C2×#88544 | 2 |
| #11720575 | 2 |
| #11720557 | 2 |
| #11720555 | 2 |
| #10592898 | 3 |
| #10588880 | 3 |